Bring a large pot of salted water to a boil and cook the pasta until just al dente, about 8-10 minutes. Drain, reserving a cup of pasta water, and set aside.
While the pasta cooks, rinse and clean the leeks thoroughly to remove any grit. Slice them into thin half-moons for even caramelization.
Heat a wide skillet over medium-low heat and add olive oil. Once shimmering, add the sliced leeks and cook slowly, stirring often, until they turn translucent and buttery, about 10-12 minutes. You should smell a sweet aroma as they soften.
Add the sliced mushrooms to the skillet with the leeks. Turn the heat to medium and cook, stirring occasionally, until the mushrooms are golden and juicy, about 8 minutes. They should release their juices and develop a rich aroma.
Mince the garlic cloves and add them to the skillet. Cook for about 30 seconds until fragrant, stirring constantly to prevent burning. The garlic should smell nutty and aromatic.
Pour in the cream or vegetable broth, stirring to combine. Let it simmer gently for 2-3 minutes until the sauce begins to thicken slightly. Taste and season with salt and pepper as needed.
Add the cooked pasta to the skillet, tossing gently to coat it evenly in the sauce. If the sauce feels too thick, splash in some reserved pasta water and stir until glossy and smooth.
Turn off the heat and sprinkle the freshly grated Parmesan over the pasta. Toss again to melt the cheese into the sauce, making it creamy and flavorful. Adjust seasoning if needed.
Let the pasta rest for a minute off the heat, then serve warm, garnished with extra Parmesan and a drizzle of olive oil if desired. Enjoy the rich, smoky flavors and tender textures.
